Prepare stock: In a 4-quart stockpot, add all stock ingredients and bring to a boil, then lower heat and simmer for 20 minutes. Strain through a one-meshed sieve into a large bowl and discard the solids. Cover the liquid and set aside.

Prepare bisque: In a stockpot, melt the butter over medium-high heat. Add the onion, carrot, and celery and cook, stirring occasionally, until softened — about 10 minutes. Add the garlic and cook for 2 more minutes. Stir in the parsley, flour, thyme, tomato paste, salt, and black pepper. Cook and continue to stir for 1 minute. Stir in the stock and bring to a boil. Reduce heat to medium-low and allow mixture to simmer for about 20 minutes. Stir in the crabmeat and red pepper and simmer for about 10 minutes. Add brandy.

Keep warm. When ready to serve, transfer to a tureen or rimmed soup bowls. Garnish with crab claws and parsley leaves.

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